Compact fiber-optic detector-array-based spectrometers (“miniature spectrometers”) pioneered by H.-E. Korth of IBM Germany and popularized most notably by Ocean Optics, Inc. have found widespread use in a multitude of applications. For example, see “A Computer Integrated Spectrophotometer for Film Thickness Monitoring,” H.-E. Korth, IBM Germany, JOURNAL DE PHYSIQUE, Colloque CIO, Supplement Number 12, Tome M, December 1983, pg. C10-101. Because the purpose of an optical spectrometer is to measure the intensity of light as a function of wavelength, the accuracy of a miniature spectrometer's responsiveness to light is of primary importance. Sources of error that can reduce accuracy and must be minimized or corrected for include detector non-linearity, scattered light (light that is scattering inside of the spectrometer's optical bench that makes its way to the detector), and second-order diffraction.
Most miniature spectrometers use diffraction gratings to spread out the light to be analyzed into its constituent wavelengths. This light is then focused onto a detector comprised of a linear array of individual detector pixels. The light that strikes a particular pixel is determined by the angle by which the light departs the diffraction grating. This angle is related to the light's wavelength by the well-known diffraction grating equation d*sin θm=m*λ, where d is the grating spacing, θm is the diffraction angle, m is an integer, and λ is the wavelength. With d being a fixed property of the diffraction grating, it can be seen that a given angle (and thus a given pixel) corresponds to multiple wavelengths, each paired with a different integer values of m.
Conventional diffraction gratings are designed so that most of the light striking the grating winds up in the “first-order beam”, which corresponds to m−1. In the ideal case of no light in the higher order beams (m>1) the light departing the diffraction grating has a unique correspondence between the wavelength λ and the angle θ (and thus the detector pixels). In practice, however, some appreciable amount of light makes it into the second-order beam, so that the light striking a particular pixel can be a combination of light from the first- and second-order beams. For example, the pixel that receives λ=1000 nm first-order (m=1) light might also receive λ=500 nm second-order (m=2) light. Light of different wavelengths is indistinguishable to the detector pixels, so the resultant intensity of light detected by the pixel (and thus reported to the user by the spectrometer) is an unknown mixture of the two wavelengths. Because the purpose of any optical spectrometer is to measure the intensity of light as a function of wavelength, this mixing of light of different wavelengths is a source of error.
To avoid the problem of second-order diffraction, some spectrometers simply measure over less than a factor of two in wavelength range (e.g., 400-800 nm) and restrict shorter wavelengths from entering the spectrometer (or at least reaching the detector). Since the majority of spectrometer uses require a greater wavelength range than allowed by this method, most miniature spectrometers block second-order light from reaching the detector array by aligning a linearly-graded optical high-pass filter in front of the array. The high-pass cutoff of the filter must be graded along the direction of the detector array because different pixels detect different wavelengths and thus require different second-order light to be either passed or filtered out.
Linearly-graded high-pass filters work well to remove second-order light in practice and are manufactured into tens of thousands of spectrometers a year. However, the linear grading makes the filters expensive to produce (approximately $100 each) and they require careful alignment to the detector during the spectrometer's manufacture.